Magnetohydrodynamics of trickle bed reactors: Mechanistic model, experimental validation and simulations

An isothermal one-dimensional two-fluid magnetohydrodynamic (MHD) model based on the volume average mass, charge, and momentum balance equations and the Maxwell's equations coupled via the Lorentz force and Ohm's law was developed for the prediction of the two-phase pressure drop and the total liquid holdup in trickle bed reactors experiencing a homogeneous transverse magnetic field. The slit model approximation and the drift flux Kozeny-Carman approach were extended for the derivation of appropriate drag force closures required in the conservation equations, respectively, in the trickle flow regime and in the dispersed bubble flow regime. The expression of liquid-solid drag was adapted to take into account the influence of the magnetic field on the laminar term and the damping of turbulent/inertial term via the Hartman number and the liquid-to-bed electrical resistance ratio. Associating these drag forces with the proposed model resulted in a fully predictive MHD approach for trickle beds. Several model limiting formulations were derived for an electrically conducting fluid flowing downwards with a stagnant gas (pure trickle flow) to yield liquid holdup, as well as for single-phase upward conditions to yield the single-phase pressure drops.